19 research outputs found

    Efficient three-dimensional geometrically nonlinear analysis of variable stiffness composite beams using strong unified formulation

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    The use of composite laminates for advanced structural applications has increased recently, due in part to their ability for tailoring material properties to meet specific requirements. In this regard, variable stiffness (VS) designs have potential for improved performance over constant stiffness designs, made possible by fibre placement technologies which permit steering of the fibre path to achieve variable in-plane orientation. However, due to the expanded, large design space, computationally expensive routines are required to fully explore the potential of VS designs. This computational requirement is further complicated when VS composites are deployed for applications involving nonlinear large deflections which often necessitate complex 3D stress predictions to accurately account for localised stresses. In this work, we develop a geometrically nonlinear strong Unified Formulation (SUF) for the 3D stress analysis of VS composite structures undergoing large deflections. A single domain differential quadrature method-based 1D element coupled with a serendipity Lagrange-based 2D finite element are used to capture the kinematics of the 3D structure in the axial and cross sectional dimensions, respectively. Predictions from SUF compare favourably against those in the literature as well as with those from ABAQUS 3D finite element models, yet also show significant enhanced computational efficiency. Results from the nonlinear large deflection analysis demonstrate the potential of variable stiffness properties to achieve enhanced structural response of composite laminates due to the variation of coupling effects in different loading regimes

    A mixed hexahedral solid-shell finite element with self-equilibrated isostatic assumed stresses for geometrically nonlinear problems

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    Mixed Finite Elements (FEs) with assumed stresses and displacements provide many advantages in analysing shell structures. They ensure good results for coarse meshes and provide an accurate representation of the stress field. The shell FEs within the family designated by the acronym Mixed Isostatic Self-equilibrated Stresses (MISS) have demonstrated high performance in linear and nonlinear problems thanks to a self-equilibrated stress assumption. This article extends the MISS family by introducing an eight nodes solid-shell FE for the analysis of geometrically nonlinear structures. The element, named MISS-4S, features 24 displacement variables and an isostatic stress representation ruled by 18 parameters. The displacement field is described only by translations, eliminating the need for complex finite rotation treatments in large displacements problems. A total Lagrangian formulation is adopted with the Green–Lagrange strain tensor and the second Piola–Kirchhoff stress tensor. The numerical results concerning popular shell obstacle courses prove the accuracy and robustness of the proposed formulation when using regular or distorted meshes and demonstrate the absence of any locking phenomena. Finally, convergences for pointwise and energy quantities show the superior performance of MISS-4S compared to other elements in the literature, highlighting that an isostatic and self-equilibrated stress representation, already used in shell models, also gives advantages for solid-shell FEs.</p

    Variable angle tow composites in fibre-reinforced polymer bridges

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    Fibre reinforced polymers are increasingly used in bridge structures for reducing their environmental impact, extending the service life and saving costs. In this work, we propose the use of composite laminates called Variable Angle Tow (VAT) to realise bridge structures. In VAT composite laminates, the fibre orientation changes pointwise over the structure, enhancing stiffness tailoring capabilities with respect to traditional straight fibre (SF) laminates. In aerospace engineering, VAT composites have been successfully used to tailor structures’ stiffness to enhance linear elastic response, reduce buckling phenomena, and optimise the postbuckling behaviour. However, VAT laminates have never been applied in civil structures. This work shows how using VAT composite laminates in a bridge girder improves its buckling and postbuckling behaviours and increases its overall stiffness. A numerical investigation is conducted to assess the benefits given by VAT composite laminates to the structural performance of bridge girders. For different spans, results of a multi-objective optimisation considering both traditional SF and VAT laminates are presented. It is found that VAT laminates exhibit a buckling load up to 80% over SF laminates, with equal or lower deflections and without adding extra material, thereby opening new design scenarios for bridge structures.</p

    A geometrically nonlinear Hellinger–Reissner shell element for the postbuckling analysis of variable stiffness composite laminate structures

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    Abstract Variable stiffness (VS) composite laminates provide larger freedom to design thin-walled structures than constant stiffness (CS) composite laminates. They showed to allow the redistributing of stresses, improving buckling and post-buckling performance and, therefore, reducing material weight and costs. This work extends a recently developed mixed shell element, MISS-4C, to the post-buckling analysis of VS composite laminate structures. MISS-4C has a linear elastic closed-form solution for the stress interpolation of symmetric composite materials. Its stress feld interpolation is obtained by the minimum number of parameters, making it an isostatic element. Moreover, its kinematic is only assumed along its contour, leading to an efficient evaluation of all operators obtained through analytical integration along the element contour. MISS-4C uses a corotational approach within a fast multi-modal Koiter algorithm to efficiently obtain the initial post-buckling response of VS composite laminate structures.</p

    Flexible hinges in orthotropic cylindrical shells facilitated by nonlinear elastic deformations

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    Flexible hinges enable the design of folding structures without using mechanisms by making use of intrinsic structural characteristics in the action of folding. This technology introduces potential benefits including weight reduction, omission of lubrication and potentially better system reliability. To achieve such technology, we exploit a well‐known structural instability characteristic of thin‐walled structures under bending: the Brazier effect. Composite materials play a key role in this problem since they enable the critical load for folding to be tuned. Moreover, the minimisation of the Brazier moment is material dependent, offering extra degrees of freedom for morphing purposes. The present work considers the minimisation of the Brazier moment providing insights on its material dependency. For this purpose, an analytical solution for cylindrical shells made of uni directional laminates and an empirical expression useful for design purposes, comprising 4‐ply symmetric laminates, are presented with validation accomplished using finite element analysis

    Morphing of symmetric cross-ply cylindrical shells by minimising the brazier moment: Optimised hinge folding

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    Aerospace and industries where both localised compliance and weight savings play a central role in design can benefit from using flexible hinges. These morphing structures use no mechanical hinges for folding. They fold by exploiting the limit point, i.e. the Brazier moment, of a geometrically nonlinear structural response characteristic of thin-walled beams under bending. Therefore, a smaller Brazier moment induces smaller non-classical stresses in the hinge during folding. Two aspects make cross-ply laminates attractive for designing flexible hinges. Firstly, the difference between the Brazier moment of an optimal symmetric generic laminate and that of an optimal symmetric cross-ply is relatively small. Secondly, cross-ply laminates do not exhibit extension-shear or bend-twist couplings which can induce complex deformations which can present challenges during design, especially considering that available analytical solutions of the Brazier moment neglect their effects. Driven by these premises, this work contributes to the preliminary design of flexible hinges by offering an analytical solution of the optimum symmetric cross-ply laminate for minimising the Brazier moment, which is subsequently validated through geometrically nonlinear finite element analysis. Moreover, this work provides insights into the prediction of the folding load considering the effects of local buckling instabilities

    Effect of potting support design on compression buckling of composite  cylindrical shells

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    The design of thin-walled cylindrical shells under compression loading is mostly driven by buckling considerations. However, accurate experimental evaluation of the buckling load is challenging due to small variations in boundary conditions due to manufacturing tolerances in support conditions. To test a cylindrical shell under compression loading, potting support is usually created around its bottom circumference to avoid edge crippling that could otherwise drastically reduce its critical buckling load. Therefore, investigating the effects of the potting support on the buckling response of cylindrical shell structures is important to mimic boundary conditions as close as possible to real structural constraints of the boundary. The main objective of this work is to investigate the effects of single and double-sided potting supports on the critical linear buckling load of composite cylindrical shells under compression loading. Then, this paper provides insights into understanding underlying reasons for the deviations of theoretical buckling loads from their corresponding experimental values due to boundary conditions, which can occur independently from, or in combination with, geometric imperfection sensitivity. Finally, robust linear buckling expressions that can help designers estimate the reduction due to support conditions are presented. These expressions can be used for evaluating initial safety margins for the potting support design used for testing  cylindrical shells. </p

    Bend-free design of ellipsoids of revolution using variable stiffness composites

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    Shells are commonly used in many structural applications due to their high specific load carrying capabilities. One of the most interesting features of shell structures is that they can resist external transverse loads by developing membrane stresses in the small deformation regime yet, in general, also generate inefficient bending deformations and stresses. In this study, a composite ellipsoid shell of revolution, under internal pressure, is designed for zero bending and curvature change. To this end, the stiffness properties of elliptical composite shell structures are tailored by fibre steering. A new definition for a bend-free state, independent of internal pressure, is presented. Based on this definition, the internal pressure-induced bending state of an isotropic ellipsoidal shell of revolution is compared with its tailored composite counterpart. Results show that up to a specific level of ellipticity, a bend-free state is achievable by fibre steering in elliptical composite shells of revolution. Finally, a failure study is performed to assess the potential improvement of the maximum allowable internal pressure by bend-free design
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